Question

Let $A\in \mathcal {M}_n(\mathbb{F}_2)$ such that $A^3=I$. Find $\det(A)$

score 77 · Answer 1 · 2026-03-25 17:40:46

77

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Let $A\in \mathcal {M}_n(\mathbb{F}_2)$ such that $A^3=I$. Find $\det(A)$

Published on 25 Mar 2026 - 17:40

score 1.2k · Answer 2 · 2026-03-19 21:51:55

1.2k

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Does the product of singular values of a rectangular matrix have a simple expression?

Published on 19 Mar 2026 - 21:51

score 472 · Answer 3 · 2026-03-25 11:01:39

472

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Matrix space $ M = \{ A \in R^{3x3};C(A) \subseteq span \{(1,2,3)^{T}\}\} $

Published on 25 Mar 2026 - 11:01

score 224 · Answer 4 · 2026-03-25 12:15:30

224

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When does collection of affine subsets of vector space have non-empty intersection?

Published on 25 Mar 2026 - 12:15

score 967 · Answer 5 · 2026-03-24 20:30:29

967

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detecting minimum and maximum using matrix calculus

Published on 24 Mar 2026 - 20:30

score 1.1k · Answer 6 · 2018-01-28 00:59:17

1.1k

Views

Finding an orthonormal basis of a span over a set of polynomials?

Published on 28 Jan 2018 - 0:59

score 147 · Answer 7 · 2026-03-25 12:49:16

147

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Let A be a square complex matrix. Show that I-A^(m+1) = (I-A)(I+A+...+A^m).

Published on 25 Mar 2026 - 12:49

score 170 · Answer 8 · 2026-03-25 17:42:23

170

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Let $A\in \mathbb{R}^{n\times n}$ be invertible such that $A$ and $A^{-1}$ have integer entries. Prove that $\det(A)\in\{-1,1\}$.

Published on 25 Mar 2026 - 17:42

score 12k · Answer 9 · 2026-03-22 07:11:48

12k

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Mathematicians' Tensors vs. Physicists' Tensors

Published on 22 Mar 2026 - 7:11

score 1k · Answer 10 · 2026-03-25 12:46:18

1k

Views

Linearly Independent Vectors Proof

Published on 25 Mar 2026 - 12:46

score 6.4k · Answer 11 · 2026-03-23 02:20:33

6.4k

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How to Find Moore Penrose Inverse

Published on 23 Mar 2026 - 2:20

score 49 · Answer 12 · 2026-03-25 09:29:55

49

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Show that the statements "$v_1 + v_2 = 0 \Rightarrow v_1 = v_2 = 0$" and "if $v \in V_1 \cap V_2$, then $v = 0$" are equivalent.

Published on 25 Mar 2026 - 9:29

score 1.5k · Answer 13 · 2026-03-22 03:01:07

1.5k

Views

Directional derivative matrix representation

Published on 22 Mar 2026 - 3:01

score 948 · Answer 14 · 2026-03-26 03:21:53

948

Views

Prove $\max_X tr(X^TAX) = $ k largest eigenvalues of $A$ for real, symmetric $A$ and $X^TX=I$

Published on 26 Mar 2026 - 3:21

score 51 · Answer 15 · 2018-01-28 06:52:45

51

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If we have a set of n linearly independent vectors in $R^n$, does that mean they span $R^n$?

Published on 28 Jan 2018 - 6:52

List Question

Let $A\in \mathcal {M}_n(\mathbb{F}_2)$ such that $A^3=I$. Find $\det(A)$

Does the product of singular values of a rectangular matrix have a simple expression?

Matrix space $ M = \{ A \in R^{3x3};C(A) \subseteq span \{(1,2,3)^{T}\}\} $

When does collection of affine subsets of vector space have non-empty intersection?

detecting minimum and maximum using matrix calculus

Finding an orthonormal basis of a span over a set of polynomials?

Let A be a square complex matrix. Show that I-A^(m+1) = (I-A)(I+A+...+A^m).

Let $A\in \mathbb{R}^{n\times n}$ be invertible such that $A$ and $A^{-1}$ have integer entries. Prove that $\det(A)\in\{-1,1\}$.

Mathematicians' Tensors vs. Physicists' Tensors

Linearly Independent Vectors Proof

How to Find Moore Penrose Inverse

Show that the statements "$v_1 + v_2 = 0 \Rightarrow v_1 = v_2 = 0$" and "if $v \in V_1 \cap V_2$, then $v = 0$" are equivalent.

Directional derivative matrix representation

Prove $\max_X tr(X^TAX) = $ k largest eigenvalues of $A$ for real, symmetric $A$ and $X^TX=I$

If we have a set of n linearly independent vectors in $R^n$, does that mean they span $R^n$?

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